https://wikimd.com/index.php?action=history&feed=atom&title=Coordinate_system 2026-04-09T02:28:07Z Revision history for this page on the wiki MediaWiki 1.44.2 https://wikimd.com/index.php?title=Coordinate_system&diff=5632065&oldid=prev 2024-04-19T19:46:59Z

<p>CSV import</p> <p><b>New page</b></p><div>[[File:3D_Spherical.svg|3D Spherical|thumb]] [[File:Number-line.svg|Number-line|thumb|left]] [[File:Cylindrical_Coordinates.svg|Cylindrical Coordinates|thumb|left]] [[File:Parabolic_coordinates_3D.png|Parabolic coordinates 3D|thumb]] &#039;&#039;&#039;Coordinate system&#039;&#039;&#039; is a system that uses one or more [[numbers]] or [[coordinates]] to uniquely determine the position of a point or other geometric element on a [[manifold]] such as [[Euclidean space]]. The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in &quot;the x-coordinate&quot;. The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a [[commutative ring]]. The use of a coordinate system allows problems in [[geometry]] to be translated into problems about numbers and vice versa; this is the basis of [[analytic geometry]].<br /> <br /> ==Types of Coordinate Systems==<br /> The most common coordinate systems are the two-dimensional [[Cartesian coordinate system]] and the three-dimensional Cartesian coordinate system, which are used to define the position of a point in space. However, there are many other types of coordinate systems that are used in mathematical and scientific applications, including:<br /> <br /> * [[Polar coordinate system]]: A two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.<br /> * [[Cylindrical coordinate system]]: A three-dimensional coordinate system that extends polar coordinates by adding a height element.<br /> * [[Spherical coordinate system]]: A three-dimensional coordinate system where each point is determined by a distance from a fixed point, an angle from a fixed direction, and an angle from a fixed plane.<br /> * [[Homogeneous coordinate system]]: Used in projective geometry, allowing for the representation of points at infinity by finite coordinates.<br /> * [[Curvilinear coordinates]]: Coordinates defined by a smoothly varying set of curves or surfaces, used in complex shapes and fields.<br /> <br /> ==Applications==<br /> Coordinate systems are used in a wide range of fields for various applications, including:<br /> <br /> * In [[physics]], to describe the motion of particles, the shape and size of fields, and the relationship between different objects in space.<br /> * In [[engineering]], for designing and constructing structures, machines, and systems.<br /> * In [[astronomy]], to locate celestial objects in the sky.<br /> * In [[geography]] and [[geodesy]], for mapping the surface of the Earth and other celestial bodies.<br /> * In [[computer graphics]] and [[computer-aided design (CAD)]], for modeling and rendering objects and scenes.<br /> <br /> ==History==<br /> The concept of coordinate systems can be traced back to ancient civilizations, but the modern Cartesian coordinate system was developed by [[René Descartes]] in the 17th century, which laid the foundation for analytic geometry and has profoundly influenced the development of modern mathematics and physics.<br /> <br /> ==See Also==<br /> * [[Vector space]]<br /> * [[Linear algebra]]<br /> * [[Geometry]]<br /> * [[Analytic geometry]]<br /> <br /> [[Category:Mathematics]]<br /> [[Category:Geometry]]<br /> [[Category:Coordinate systems]]<br /> <br /> {{math-stub}}</div>

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